二维MOC Krylov子空间迭代的CMFD预条件子研究

Research on CMFD Preconditioner for Two-dimensional MOC Krylov Subspace Iteration

为了提高二维特征线(MOC)Krylov子空间迭代的效率,提出了基于粗网有限差分(CMFD)矩阵的预条件子。研究首先将CMFD加速方法进行线性化,推导出线性CMFD预条件子;其次将线性CMFD预处理Krylov子空间方法用于求解二维MOC方程;最后利用IAEA LWR和2D C5G7基准题对线性CMFD预条件子的加速性能进行了测试。结果表明:在应用CMFD预条件子后,IAEA LWR基准题的迭代次数减少了52.7%,计算时间减少了41.8%;2-D C5G7基准题的迭代次数减少了20.3%,计算时间减少了13.2%;研究还发现CMFD预条件子对于局部非均匀性不强的问题效果很好,对于局部非均匀性较强的问题性能下降。

To improve the efficiency of the Krylov subspace iteration for two-dimensional method of characteristics(MOC),a preconditioner based on the coarse-mesh finite difference(CMFD)matrix is proposed.Firstly,the CMFD acceleration method is linearized and the linear CMFD preconditioner is derived.Secondly,the linear CMFD preconditioner is applied to the Krylov subspace method to solve the two-dimensional MOC equation.Finally,the acceleration performance of the linear CMFD preconditioner is tested using the IAEA LWR and 2-D C5G7 benchmarks.The results show that,after applying the CMFD preconditioner,the iteration count for the IAEA LWR benchmark is reduced by 52.7%,and the computational time is decreased by 41.8%.For the 2-D C5G7 benchmark,the iteration count is reduced by 20.3%and the computational time is reduced by 13.2%.The study also finds that the CMFD preconditioner works well for problems with weak local heterogeneities,but its performance decreases for problems with strong local heterogeneities.